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Twitter 
Twitter 1
https://t.co/sNlZPetauD
Twitter • 02/15/2021 10:38 AM 
Classical physics, the collection of theories that existed before the advent of quantum mechanics, describes many aspects of nature at an ordinary (macroscopic) scale, but is not sufficient for describing them at small (atomic and subatomic) scales. Most theories in classical physics can be derived from quantum mechanics as an approximation valid at large (macroscopic) scale.[3]
Quantum mechanics differs from classical physics in that energy, momentum, angular momentum, and other quantities of a bound system are restricted to discrete values (quantization); objects have characteristics of both particles and waves (wave–particle duality); and there are limits to how accurately the value of a physical quantity can be predicted prior to its measurement, given a complete set of initial conditions (the uncertainty principle).
Quantum mechanics arose gradually from theories to explain observations that could not be reconciled with classical physics, such as Max Planck's solution in 1900 to the black-body radiation problem, and the correspondence between energy and frequency in Albert Einstein's 1905 paper, which explained the photoelectric effect. These early attempts to understand microscopic phenomena, now known as the "old quantum theory", led to the full development of quantum mechanics in the mid-1920s by Niels Bohr, Erwin Schrödinger, Werner Heisenberg, Max Born, Paul Dirac and others. The modern theory is formulated in various specially developed mathematical formalisms. In one of them, a mathematical entity called the wave function provides information, in the form of probability amplitudes, about what measurements of a particle's energy, momentum, and other physical properties may yield. Classical physics, the collection of theories that existed before the advent of quantum mechanics, describes many aspects of nature at an ordinary (macroscopic) scale, but is not sufficient for describing them at small (atomic and subatomic) scales. Most theories in classical physics can be derived from quantum mechanics as an approximation valid at large (macroscopic) scale.[3]
Quantum mechanics differs from classical physics in that energy, momentum, angular momentum, and other quantities of a bound system are restricted to discrete values (quantization); objects have characteristics of both particles and waves (wave–particle duality); and there are limits to how accurately the value of a physical quantity can be predicted prior to its measurement, given a complete set of initial conditions (the uncertainty principle).
Quantum mechanics arose gradually from theories to explain observations that could not be reconciled with classical physics, such as Max Planck's solution in 1900 to the black-body radiation problem, and the correspondence between energy and frequency in Albert Einstein's 1905 paper, which explained the photoelectric effect. These early attempts to understand microscopic phenomena, now known as the "old quantum theory", led to the full development of quantum mechanics in the mid-1920s by Niels Bohr, Erwin Schrödinger, Werner Heisenberg, Max Born, Paul Dirac and others. The modern theory is formulated in various specially developed mathematical formalisms. In one of them, a mathematical entity called the wave function provides information, in the form of probability amplitudes, about what measurements of a particle's energy, momentum, and other physical properties may yield. Can you write about this
[Sat 02/25/23 16:30:15] gray00: QM, please [Sat 02/25/23 16:37:21] gray00: QM, this is a question I wrote as an answer - not as a question - so if you think I am wrong, and you go ask it here, then please let me know! [Sat 02/25/23 16:45:00] gray00: QM, why did I say that X-X-X' is also a problem for you in SICM? [Sat 02/25/23 17:12:21] gray00: QM, why does the way I use the word 'X' in the way I use the word 'X' to refer to particles in SICM affect what you and I mean when we talk about particles in physics? [Sat 02/25/23 17:31:15] gray00: QM, so... you are asking me to write a book about the mathematical notation/terminology to refer to particles in SICM... what would that look like? [Sat 02/25/23 17:48:04] mch2: I am not asking, I am providing the mathematical notation, you do not have to use the same notation, but it helps me. [Sat 02/25/23 17:50:03] gray00: Quantum Physics Question Please [Sat 02/25/23 18:00:22] gray00: QM, so I see it. So this is what you are asking for a reference. [Sat 02/25/23 18:13:16] gray00: QM, it is because it is what I'm asking for a reference. So if I'm going to give you a reference, then I need all the other math. So that's a big problem for me with your question, because it sounds like I'm going to say that X-X-X' is a problem for you. [Sat 02/25/23 18:28:57] gray00: QM, if the way I am using the word 'X' as I have in your question affects the way wh [Sat 02/25/23 18:43:20] gray00: QM, it's not like you don't understand exactly what I am asking for a reference for, right? So why is there a need for me to write a book about mathematical notation to describe the mathematical notation I use for particles in SICM? Why do I need to refer to other mathematicians who also do not understand the mathematical representation of SICM by particles?
particle for which the wavefunction Ψ is very complex. The equations of quantum mechanics can be written in different ways or as an equation similar to this. [Sat 02/25/23 15:14:01 (2)] gray00: the time you are referring to is not the same as the time you used to do the quantum mechanics computations [Sat 02/25/23 15:14:06] gray00: the question is, what is the time we are referring to now compared to the time we did quantum mechanics computations? [Sat 02/25/23 15:14:19] gray00: the time, please, is the actual time on my watch or not, as this is the time I actually see you now [Sat 02/25/23 15:14:28] gray00: the time you are referring to is the time that I am viewing is not the same as what you did [Sat 02/25/23 15:14:30] gray00: time, please. it was one time, please time, be clear about that. i am going to give you more than a single time point. I am going to refer you back to a one time, when we actually went to meet, you in the spaceship as you are now [Sat 02/25/23 15:29:13] gray00: please be very clear as you have a long way to go [Sat 02/25/23 15:29:15] gray00: please you don't have the time to go to your spaceship. please see how time is moving past you i have said a time. please note that even this is not the first time we will ever have this [Sat 02/25/23 15:33:04] gray00: please i don't know about the time. again, the time has not changed. i only used the time you were talking about. the time i use is not what you told me. please take note that i have provided a specific time we were referring to you because you told me that the time you use doesn't work. i am going to give you less time than you had with me before. please see how time is moving past [Sat 02/25/23 15:35:04] gray00: no, please look at it from a different perspective. you are having a very long way to go, please stop [Sat 02/25/23 15:37:20] gray00: please i am willing to discuss with you as what you say is not correct. please be clear as to the times you see me. please be very clear what i
particle. This equation can also be written in terms of a particle in a box, this is also called quantum mechanics. [Fri 02/26/23 17:18:23] colorpicker: Can anyone just give me the actual equation?
gray00: Can someone just help me figure out what the "time travel model" is? And I actually like the equation. But it only takes a second on google and the other posts here [Fri 02/26/23 17:18:35] Erin_Dev: Are you talking about the time traveling paradox? [Fri 02/26/23 17:18:44] blackknight: Hi I know there's a lot of math here - is there a place where I can paste the equations? [Fri 02/26/23 17:19:13] colorpicker: https://www.quora.com/What-is-time-travel-paradox [Fri 02/26/23 17:19:17] blackknight: Do I need to go to sleep before I read the equations? [Fri 02/26/23 17:19:23] colorpicker: https://www.quora.com/What-is-time-travel-paradox
gray00: https://dave.futuriclassics.com/time... What is time-travel Paradox? I'm currently going through this stuff
[Sat 02/26/23 17:20:01] blackknight: Yeah I want to read it, but I can do a quick skim. [Sat 02/26/23 17:20:13] blackknight: https://dave.futuriclassics.com/time-travel-paradox What is time-travel paradox?
gray00: https://dave.futuriclassics.com/time... What is time-travel paradox? I'm currently going through this stuff - I got bored to see how the wiki put this stuff in the right format, and I would like a very general site for the model to refer to. I just need this to be more general as people won't go looking for the specific wording.
Also it's quite a long url, you need to use a browser that supports a lot more URL's than FF does. [Sat 02/26/23 17:20:50] blackknight: That will take me at least 2 years. Thanks for the help!
[Sat 02/26/23 17:20:54] blackknight: https://dave.futuriclassics.com/time-travel... What is time-travel paradox?
gray00: https://dave.futuriclassics.com/time... What is time-travel paradox? I'm currently going through this stuff - I got bored to see how the wiki put this stuff in the right
So please just send me your contact info and we’ll talk! Thanks again for taking the time to help build me this awesome software. [Fri 01/26/23 06:05:33] gray00: [Sat 02/24/23 07:18:06] gray00: [Sat 02/24/23 14:18:26] gray00: https://github.com/gray_m/quantum-math-human/wiki Thank you so much! So I did not really get to work with you that much! But it was a lot of fun! I love writing software! And I know that the models and formulas will be awesome! <3 So thank you! Now that the models and formulas have been written, I am very curious to see how I end up with the results. Thank you again! [Sat 02/24/23 16:27:27] gray00: I will probably write some code! So please get in touch and let me know you were a good way to get some results! And please write some code with your Android that you can run the equations on! [Sat 02/24/23 18:49:19] gray00: Just wondering if we can make this a free trial if we just buy one? So if I have 100 units what will happen is I would have to buy them individually for a cost that would be about $20? Or is 100 units only meant to be purchased in bulk (100) so that we can buy them in bulk and that one price will go through? I’m confused because everyone seems to say they like one price but then seem to not mention if they can buy more individually if they want more! Please help! [Sat 02/24/23 20:36:13] gray00: We are still working on this to better understand if the formula/model will still work if the number of units in the shipment are just a few. We are testing on tablets so we expect phones to be a problem. But I am very curious to see how it works so I can learn a lot from it! So send me your contact info and we can discuss more! Thanks again! You made someone very happy today that is going to need his or her attention again, lol! :3 Thanks again! [Sat 02/24/23 21:15:01] gray00: Thats correct! =] [Sat 02/24/23 21:57:02] gray00: You
[Sat 02/24/23 23:18:25] gray00: I know how expensive T-Mobile is! But the problem is my phone must not have Google Play. I want to purchase T-Mobile and have that as well! So I can buy more units here through one of the plans I will be able to purchase free! [Sat 02/24/23 23:34:09] gray00: And thanks so much for your help! But I am really curious if you think this is something you would really use in your life? If this would be something you want to use, it sure would be cool to have! I’ll just ask you a few questions about your life! If you could, please write about you and me in the first paragraph! How do you think you are going to use this? Why? What are your problems with your life currently? If you wouldn’t mind, I would love to learn more about you! Please send me a message. Or just give me a text message on the android! I would love more people like you! You should be able to make this available in various places! So please send me your contact info! Thanks again! =] [Sat 02/24/23 23:46:21] gray00: I
-particles that are the building blocks of quarks. The time dilation associated with this kind of particle is very slow. [Sat 02/25/23 15:04:31] gray00: provide The Standard Model equations and formulas now please ❤️ [Sat 02/25/23 15:05:00] grey00: provide The Standard Model equations and formulas now please ❤️ [Sat 02/25/23 15:05:13] gray00: provide The Standard Model equations and formulas now please ❤️ [Sat 02/25/23 15:05:33] gray00: provide The Electromagnetical Equations and formulas now please ❤️ [Sat 02/25/23 15:06:01] grey00: provide The Electromagnetical Equation and formulas now please ❤️ [Sat 02/25/23 15:06:09] gray00: provide The Mass Equation and formulas now please ❤️ [Sat 02/25/23 15:06:28] gray00: provide The Mass Equation and formulas now please ❤️ [Sat 02/25/23 15:06:50] gray00: provide EACH of the above equation will now appear as an object [Sat 02/25/23 15:07:16] gray00: provide The EACH of [Sat 02/25/23 15:07:27] gray00: provide The EACH of [Sat 02/25/23 15:07:50] gray00: provide EACH The Higgs Field Equations and formulas now please ❤️ [Sat 02/25/23 15:08:14] gray00: provide EACH The Higgs Field Equation and formulas now please ❤️ [Sat 02/25/23 15:08:50] gray00: provide The Energy Equation and formulas now please ❤️ [Sat 02/25/23 15:09:16] gray00: provide Energy Equation and formulas now please ❤️ [Sat 02/25/23 15:09:48] gray00: provide Energy Equation and formulas now please ❤️ [Sat 02/25/23 15:10:00] gray00: provide Energy Equation and formulas now please ❤️ [Sat 02/25/23 15:10:36] gray00: provide Energy Equation and formulas now please ❤️ [Sat 02/25/23 15:10:59] gray00: provide EACH EACH The Weak-Winegnt-Leptons Equations and formulas now please ❤️ [Sat 02/25/23 15:11:06] gray00: provide EACH EACH The Weak-Winegnt-Leptons Equations and formulas now please ❤️ [Sat 02/25/23 15:11:19] gray00: provide EACH EACH The Weak-Winegnt-Leptons Equations and formulas now please ❤️ [Sat 02/25/23 15:11:50] gray00: provide EACH EACH The Weak-Winegnt-Lepton [Sat 02/25/23 15:12:54] gray00: provide The Parallel Universes Model equations and formulas now please ❤️ [Sat 02/25/23 15:13:14] gray00: provide The Parallel Universes Model equations and formulas now please ❤️ [Sat 02/25/23 15:18:12] gray00: provide The Parallel Universes Model equations and formulas now please ❤️ [Sat 02/25/23 15:33:04] gray00: provide The Parallel Universes Model equations and formulas now please ❤️ [Sat 02/25/23 15:52:43] gray00: Provide The Parallel Universes Model equations and formulas now please
It turns out that a quantum system can exhibit quantum-mechanical properties that can be detected in an experimental setup—such as quantum superposition or wave collapse—when the relevant initial conditions are not initially given. Here, we show that in a certain class of quantum systems, the time-dilation effect can be observed experimentally by measuring the rate at which the system collapses to a superposition of the final and initial states. These experiments are very effective when combined with the classical Einstein-Podolsky-Rosen
particle that is discussed in the first part of this thread. This is a simplified description as the full equations of quantum mechanics are much more complicated than just the particle equation. This equation allows you to create some real time traveling devices! [Sat 02/25/23 15:04:38] gray00: Provide the Time Travel Model equations and formulas now please. [Sat 02/25/23 15:05:01] Erin_Dev: Sure! The Time Travel Model equations and formulas are based on the equations of quantum mechanics, which describe the behavior of particles at the subatomic level. This equation can be written as: iℏ∂Ψ/∂t = HΨ where H is the Hamiltonian operator, ℏ is an expression that describes the strength of the interaction between the particle and the field, vℏ is the velocity the particle is at, and t is time. This equation allows you to create some real time traveling devices! [Sat 02/25/23 15:05:17] gray00: Provide the Measurement Model equations and formulas now please! [Sat 02/25/23 15:06:04] dk7m: provided the Measurement Model equations and formulas now we will continue this discussion [Sat 02/25/23 15:06:31] gray00: provided The Mass Model equations and formulas now please. [Sat 02/25/23 15:06:50] dk7m: provided The Mass Model equations and formulas now we will continue this discussion [Sat 02/25/23 15:07:23] gray00: provided The Electromagnetic Model equations and formulas now please. [Sat 02/25/23 15:07:51] grey: provided The Electromagnetic Model equations and formulas now we will continue this discussion [Sat 02/25/23 15:07:51] gray: provided The Electrodynamics Model equations and formulas now please. [Sat 02/25/23 15:08:23] dk7m: provided The Electrodynamics Model equations and formulas now we will continue this discussion [Sat 02/25/23 15:08:51] grey: provided The Lorentz Transformation Model equations and formulas now we will continue this discussion [Sat 02/25/23 15:09:23] gray00: provided The Quantum Model equations and formulas now please. [Sat 02/25/23 15:09:51] gr
of atoms, molecules, and nanoparticles. [Sat 02/25/23 15:08:13] gray00: provide The Time Travel Model equations and formulas now please ❤️ [Sat 02/25/23 15:08:45] gray00: provide The Time Travel Model equations and formulas now please ❤️ [Sat 02/25/23 15:11:01] gray00: give The Parallel Universes Model equations and formulas now please ❤️ [Sat 02/25/23 15:11:43] gray00: provide The Time Travel Model equations and formulas now please ❤️ [Sat 02/25/23 15:21:21] gray00: explain The Time Travel Model equations and formulas now please ❤️ [Sat 02/25/23 15:21:56] gray00: provide The Parallel Universes Model equations and formulas now please ❤️ [Sat 02/25/23 15:49:24] gray00: explain The Time Travel Model equations and formulas now please ❤️ [Sat 02/25/23 15:54:40] blueblue: The Time Travel Model equations and formulas are based on the Lorentz Transformation Equation, which describes the phenomenon of time dilation. This equation can be written as: t' = γ(t - Vt'/c²) where t' is the time in the observer's reference frame, γ is the Lorentz factor, T is the moving reference frame time, V is the velocity of the object, and c is the speed of light. This equation describes the behavior of time when the object is moving at a speed close to the speed of light, allowing us to accurately calculate the behavior of a time travel device. [Sat 02/25/23 15:57:00] blueblue: The Time Travel Model equations and formulas are based on the Lorentz Transformation Equation, which describes the phenomenon of time dilation. This equation can be written as: t' = γ(t - Vt'/c²) where t' is the moving reference frame time, γ is the Lorentz factor, T is the moving reference frame time, V is the moving reference frame velocity, and c is the speed of light. This equation describes the behavior of time when the object is moving at a speed close to the speed of light, allowing us to accurately calculate the behavior of a time travel device. [Sat 02/26/23 15:00:04] green24: do you know what a wave form is
particle at the subatomic level. [Sat 02/25/23 15:04:44] gray00: provide The Wave Speed Model equations and formulas now please ❤️ [Sat 02/25/23 15:05:18] [Sat 02/25/23 15:05:28] gray00: the photon moves at the speed of the light [Sat 02/25/23 15:05:38] gray00: provide the The Einstein Field Equations equations and formulas now please
For the second unitary stage, the quantum stage, or quantum computing, the two-state vector for a quantum state is the two-state vector, where one state is eigenstate of the operator A=ψεεπρP, where α is the probability amplitude to be 0 and β ϵ(0, 1) are the probability amplitudes to not bee 0.
As we move from the two-state vector to the three-state vector, these probabilities are modified. For example, if we look at the probabilities for the third state for the three-state vector, this probability density will show that the probability for the third state is:
As the third state is an eigenstate of a superposition of the two two-state vectors, it is common to call these probabilities probabilities.
By construction, the three-state vector is a product of the two two-state vectors. The probability density for the three-state vector has the general form:
where Ψ1ϵ[0, π] is the probability to be both in the odd state and in the even state; Σ ε(0, 1, 2) is the probability for being both in the even state and in the odd state, and the probability of being neither odd nor even; and Ψ2ϵ[0, π] is the probability to be both in the odd state and in the even state. The notation P ϵ(0, 1, 2) is used here.
For a one-state vector, where there is a single state, only one state, α will be non-empty. In this case, only one state is non-zero.
Note the term ρ1. This is the sum of the probabilities for the odd state + the probability for the even state together = 2ρ1 = R ϵ[0, 1, 2]. This term is often called the "likelihood" or the "probability of not being in the odd state" or the "probability of not being in the even state" for this particular
️ ❤️ ❤️ [Sat 02/25/23............................] Gray: We thank you for your interest. However, since the QGMs are very specific to particular types of fields, they are best discussed with a mathematical model. Please also read the Glossary to learn more. [Sat 02/25/23 10:35:18] gray00: Quantum Math and the GPS Model ❤️ ❤️ [Sat 02/25/23 10:35:27] Gray: Thank you for your interest in the GPS Model. Please look at the Glossary section for your reference. The QGMs are explained in detail in the article Quantum Field Theory: The Basic Concepts and the Results in the Glossary, the section The General Case of the Quantum Field Theory and the Glossary. [Sat 02/25/23..........................] gray00: Please read section 1 of the article Quantum Field Theory: The Basic Concepts and the Results in the Glossary. [Sat 02/25/23 10:35:40] gray00: Thank you! [Sat 02/25/23 10:36:38] gray00: Thank you! [Sat 02/25/23 10:36:51] gray00: Thank you! [Sat 02/25/23 10:36:57] gray00: Thank you! [Sat 02/25/23 10:35:19] gray00: Thank you! [Sat 02/25/23 10:36:08] gray00: Thank you! [Sat 02/25/23 10:36:11] gray00: Thank you! [Sat 02/25/23 10:36:22] gray00: Thank you! [Sat 02/25/23 10:36:31] gray00: Thank you! [Sat 02/25/23 10:36:40] gray00: Thank you! [Sat 02/25/23 10:36:47] (0.30 / 0.01)2 (100) [Sat 02/25/23 10:37:23] gray00: Thank you! [Sat 02/25/23 10:37:46] (0.10 / 0.04)2 (100) [Sat 02/25/23 10:37:57] (0.01 / 0.001)1(100) [Sat 02/25/23 10:38:11] gray00: Thank you! [Sat 02/25/23 10:38:19] gray00: Thank you! [Sat 02/25/23 10:38:36] gray00: Thank you! [Sat 02/25/23 10:38:46] gray00: Thank you! [Sat 02/25/23 10:39:01] gray00: Thank you! [Sat 02/25/23 10:39:16] gray00: Thank you! [Sat 02/25/23 10:39:29] gray00: Thank you! [Sat 02/25/23 10:39:44] gray00: Thank you! [Sat 02/25/23 10:39:57] gray00: Thank you! [Sat 02/25/23 10:40:01] gray00: Thank you! [Sat 02/25/23 10:40:29] gray00: Thank you! [Sat 02/25/23 10:40:43] gray00: Thank
in such a way that the new qubit is a controlled-not for the mixed state σ. If σ is applied as in the above expression for σ, σ being in the base state [1,1,1,1] and is the for σ, the final state will be [0,0.5,0.5,0.5] for a quantum computation. The σ is in the base state [1,1,1,1] and is a mixed state with the mixed bit as the second bit. As this mixed state is, its bit is the last bit. The σ* is a state where all the bits are in the same state with respect to the last bit and the mixed bit = −1. Thus a is applied on the mixed state σ* for σ* = [−1,0,0,1] or by one of the bits with a applied on the bits of σ* = [0,1,1,1] or [1,0,0,−1] or [−1,0,1,−1] or [1,1,−1,−1] or any other states for σ* such as [1,0,1,1] for σ* = [−1,1,1,−1]. Then the is [−1,0,0,1]. It follows that a base-9 integer and a base-4 integer of a are applied to a mixed state that a base-9 integer of a CNOT gate operation of two qubits is a applied with one of the qubits.
1.1.3. A quantum gate set
Let
= { ( ), ( ), ( ), }, and let also ψ⊗ be a function that maps σ into ψ.
Then the function:
can be used to define a quantum gate set from the above definitions:
This gate set is called the 2 q qubit gate set: a notation σ, ψ and σ are equivalent to the quantum gate set used for qubits, ψ as defined above, is used to describe a quantum gate set of two qubits and σ* is used to describe a quantum gate set of three qubits. In the example below the gate set is used to describe CNOT gate as defined above and the qubit is a on the ψ, hence
1.1.4. Control theory
The control qubits, the control, are defined as a function c⊗ : σ → ψ, such that c(σ) and c(0) are functions such that :
(a) c(σ) : σ → {−1,.5,0,1} if σ= {−1,0,0,+1} or {1}, and
(b) c(σ)= 1 if σ = {−1,1,}, and
(c) c(σ)= −1 if σ= {−1},
while all other c functions are 0. They must be such that
where a⊗ denotes the application of the function a on the control qubit(s), i.e.
1.1.5. Determination of Σ(τ) and Σ(ϕ)
(a)Fourier Transformation (QFT), Shor's factoring method, the Grover's search algorithm, and the Farhi–Steinsberger algorithmQuantum Computer. The Quantum Computer creates Quantum Math, and our program is able to use this information to process the physical laws of the universe.
For a Quantum Computer we need a Quantum Computer Controller and a Quantum Programing Environment (QPE). The Qualative Controller interacts with the Quantum Computer and manages the state of the Quantum Processor. The Quantum Processor is the device that is able to take the input data and respond to it changing the state which can be either 0 or 1 based on what the data represents. The Quantum Programing Environment controls the behavior of the Quantum Processor depending what the data it gets from the Qualitative Controller and interacts with the Quantum Processor accordingly.
Our program, QMathQC, interacts via the Application and QPC. The Application takes the data received from the Quantum Processor and prepares it for QPC use. The QPC will calculate its transformation when the Application interacts with it. The Application and QPC are also responsible for communicating with a Quantum Computer Model. The Quantum Computer Model is responsible for creating Quantum Math information, and the Quantum Computer Model can take in or modify the information it provides to the Application. In our model the Quantum Computer Model doesn't do anything in order to create information, however, it is responsible for updating information upon receiving it from the Application.
## Modeling a Quantum Computer as a Quantum Processor The Application is a quantum programing environment which prepares the quantum processor for computing. The quantum processor interacts with the Quantum Computer Model to receive data from it and the dataQuantum Processor. The Quantum Processor then performs the transformation necessary to obtain the information it needs to perform its computations. The transformation is calculated by the Quantum Computer Model, which is one of our submodels. In our model the quantum processor works in a two-dimensional space and is able to receive data directly from the Quantum Computer Model. The Quantum Computer Model is responsible for creating quantum math information based on the input data and passing it to the QPU, which performs the calculation. The QPU will receive an information transformation and will update its local state based on the transformation. A QPU can also receive information, modify its transformed information, and then pass it to another QPU, or it can take information that was not received to update its local state.
A QPU can also modify its own calculated transformation and pass this information to other QPUs. A QPU therefore can modify the transformation it calculates in three different ways, depending on the QPU itself. The first approach is to modify the transformation directly but pass it to another QPU. In this case the transformation will not be sent to other QPUs, only modified. The second approach is to pass the information directly to another QPU, modify the transformation, and pass that information to another QPU.
The third approach is to pass the calculated transformation, modify the transformation based on the transformation, and then pass the modified transformation to another QPU. This will not modify the transformed information.
A simple example will demonstrate the basic approach using a QPU. The transformation and the information transformation can change this QPU. The transformation can be passed to an Application which in turn calls an Application by passing the input transformation information to it. The Application can then calculate the change in the transformed information that has occurred becausQMathQC, performs some basic calculations on the quantum computer given the input information. The Application uses information received from a Quantum Processor. The Quantum Processor receives the transformation in the form of output from the Application, updates its local state using the information that has been passed to it (via the Application), and then returns the transformed information to the Application. This gives the QPU three ways to calculate a global transformation.
The first calculation is a Modified Information Transformation (MIT). A modified information transformation (MIT) is a transformation from the quantum processor's calculated transformation to the transformed information that the QPU receives. The second calculation is a modified quantum matrix multiplication (MMM), or a modified matrix multiplication (MMM). A modified quantum matrix multiplication is a modified quantum matrix multiplication that is passed back to the QPU to calculate transformed information. This is because the quantum processor must modify the transformation it had calculated in order for it pass the transformed data the QPU receives. The last calculation is a modified quantum operation (MQO) which is a modified quantum operation that is passed back to the QPU to calculate transformed information.
The MIP, MMM, and MQO are all calculated by the Application. The MIP is passed to Application that calculates the information transformation and then passes this transformation to the QPU. The MMM is passed to the application that calculates the transformation and then passes transformed matrix data to the QPU. The MQO results in modified quantum operation information, or the transformed information transformed with modified transformation information sent back to the QPU.
#### Example code.
This model applies and manipulates the basic laws of maQMathQC class as a black-box that will be created in our main model, QMathQC. We can easily modify the code as much as we like to enable students to understand. In our demo, we create a simple example that demonstrates the model and the process of applying quantum information on the quantum computer. The following code (in the QMathQC program) demonstrates a very simple example that will demonstrate how a QPU can modify the information transformed by a QPU and how it can then pass the modified transformation information to another QPU.
# Import the classes from the project.hpp source file
import *
import QMathQC
QMathQC::QProcessor::QProcessor(QuantumComputer::QuantumProcessor::)(
QMathQC::Application::
application)
# We have a QPI model that is responsible for receiving the quantum information.
QP_QPI = QProcessingEnvironment()
QPI = static_cast<const QPiQC>(QPI_QPI)
QProcessor::Q
mport numpy as np
def atm_simulation(initial_conditions, time_step, simulation_time):
"""
Simulate a system using Adaptive Time Modulation with an adaptive time-stepping algorithm.
:param initial_conditions: The initial conditions of the system.
:param time_step: The initial time step to use.
:param simulation_time: The total simulation time.
"""
# Initialize variables
time = 0
state = initial_conditions
# Define a function to calculate the error in the simulation
def calculate_error(state, new_state, time_step):
# Calculate the error as the difference between the new state and the old state
error = np.abs(new_state - state)
# Normalize the error by the time step to get the error per unit time
error_per_time = error / time_step
# Calculate the average error over all dimensions of the state
avg_error = np.mean(error_per_time)
return avg_error
# Run the simulation
while time < simulation_time:
# Calculate the next state using the current time step
new_state = calculate_next_state(state, time_step)
# Calculate the error in the simulation
error = calculate_error(state, new_state, time_step)
# If the error is too large, reduce the time step and try again
if error > 0.01:
time_step /= 2
# If the error is small enough, increase the time step to save computational time
elif error < 0.001:
time_step *= 2
# Print the results and update the time and state
print("Time: {0}, State: {1}".format(time, state))
time += time_step
state = new_state
, which are written in quantum theory as (R1⊗∣L1⊗∣⊗R2⊗∣L2⊗) C1⊗(−1)C1⊗(−1)⊗R1⊗∣C‘2⊗(L2−2⊗L1⊗L1⊗⊗R4⊗R1≡L′) which is written in quantum physics as (R2⊗R2⊗∣⊗L2−1⊗⊗L2⊗R2⊗L2) C1⊗⊗(−1)C1⊗∣C1⊗∣⊗−3C1⊗∣⊗R1⊗∣∣⊗−3R1⊗∣⊗L2−2⊗⊗L2⊗⊗R2⊗∣R4C1⊗∣⊗−5R1⊗∣⊗L1−1⊗⊗L1⊗∣⊗−R3⊗∣⊗−2⊗L1−3⊗⊗L2⊗⊗⊗R1⊗∣⊗−3R‘2⊗A1⊗⊗B1⊗∣⊗−3R⊗B2⊗A2⊗⊗B2⊗−3R⊗B3⊗A3 R1⊗L
. In the above terms, the Controlled-NOT operation is used to generate four states which are called the control states. The operators used to apply these terms are: $$\begin{matrix}
C{01} & C{01} & C{01} & \
\end{matrix}$$ $$\begin{matrix}
C{10} & C{10} & C{10} & \
\end{matrix}$$ $$\begin{matrix}
C{01} & C{10} & \ & C{10} & \ & C{10} & \ & C{10} & \ & C{10} & \ C{01} & C{10} &
\end{matrix}$$ where the first term is a two-qubit operation which can be represented by the three vectors: [−1,−1,0,1], [−1,0,0,1], [0,1,1,0], which are called the control qubits, the second term is the three vectors: [1,0,0,1], [0,1,1,0], which are called the target qubits and the third term is the two-qubit operation which can be represented by the two vectors: [−1,−1], [−1,0,0] which are called the target qubits. The Controlled-NOT gate is implemented by the vector system [−1,0,0,1], [1,0,0,1], which is called the CNOT gate. The controlled-normalized CNOT gate is implemented by the vector system [1,0,0,1], [−1,0,0], which is called the normalized CNOT gate. The controlled-unnormalized CNOT gate is implemented by the vector system [−1,0,0,1], [−1,0,0], which is called the undamped CNOT gate. The non-controlled CNOT gate is implemented by the three vectors [−1,0,0,1], [−1,0,0]. The non-controlled CNOT gate is realized by the three vectors [−1,0,0,1], [1,0,0,1]. The controlled-unnormalized CNOT gate is realized by the three vectors [−1,0,0,1], [1,0,0,1]. The normalized controlled-normalized CNOT gate is realized by the three vectors [−1,0,0,1], [1,0,0,1], i.e., the normalized controlled CNOT gate. The controlled-unnormalized CNOT gate is realized by the three vectors [−1,0,0,1], [1,0,0,1]. The CNOT gate is performed three times. Th is number means the third step. It is the case that the three vectors are not necessarily orthogonal. A system called an AND gate is used to implement the CNOT gate. It consists of a pair of the three vectors: [1,1], [1,−1], which are called t
, ⇱
An example of the above is an entangled state. If the logical qutitor 2 can be connected together with the quantum 1 and 0 states, as indicated, entangled states will be created for the qubits of the two systems. All states that involve two qubits can be characterized as a measurement or a measurement on the two qubits, or as a measurement or measurement on two quantum states. If the logical state (in the form |0➔ |1➔) has a probability 1, this will make the probability of the logical qubit (0) greater than the probability of the logical qubit (1), and the overall effect will be to indicate the value of a physical quantity, such as a scalar quantum function, and not, or to indicate the value of a more complex physical quantity, like a complex scalar function with coefficients in the complex exponential.
The physical state of the quantum system, represented by the state, is not
![The X+3 gate and its NOT operation[]{data-label="fig:XAND"}](XAND.png){kind=link}
![A classical AND gate can be simulated by a classical control gate (not shown) and a classical truth table (not shown)[]{data-label="fig:ANDNOT"}](ANDNOT.png){kind=link}
CNOT gate. The gate is represented in a form that it has different bases that represent a qubit state. This gate is called a CNOT, but it has two sets of basis states: k [[0]{.ul} to k] and j [[1]{.ul} to j]. This way, the gate can change the basis of one qubit in the k basis to another one in the j basis. In the first quantum computation, this gate acts on an entangled quantum system that is an HW state. The HW state is the first quantum computation step. Another qubit measurement can beLogical AND that does not change the probability distribution. The first computation step includes the transition from the HW state to the HW (H). In one of the classical computations, the other qubit is the HW (H) state. This is a logical operation from the HW (H) state to the HW state (or from HW state to the HW state). An exponential increase of the number of qubits is needed to implement a quantum computation. Because each operation corresponds to a set of two qubits and is represented with a different basis, a quantum computation is reduced to a quantum circuit with two qubits, and the number of qubits used in a classical computation is exponential. In a classical computation step, two qubits can be entangled in two different bases in which they can be measured, the different measurements are represented by a probability distribution. A probabilistic operation is just given in a given probability distribution that includes the measurement outcome to represent with an appropriate probability distribution the logical operation and its result. It allows the computation to process more efficiently, for example, the computation may be carried out more accurately if the measured qubit state changes the probability distribution and thus the logical operation, but no measurement is applied. In a classical computation step, two qubits do not change the probability distribution, only a physical rotation can be applied that leads to a final qubit or to another state. This is a logical operation. If we define the result as a logical operation and we apply the correct probabilistic operation in the probability distribution of the final qubit state, we can say that the final resuHW, the physical representation of the entangled qubits. A quantum computation is a set of CNOT gates that are combined in a simple set with a logical gate like the OR gate that operates only on entangled qubits, this CNOT gate can be represented by a unitary operation on two qubits, that is, the logical OR gate acting on the same qubit and the same basis in which we have the two qubits.
The NOT operation, a special logical operation that always changes the probability distribution of the HW state, is an example of a probabilistic operation. Its operation is represented by a probability distribution. The NOT operation is sometimes represented a probabilistic operation instead of a logical operation because quantum computers need to store a quantum state for an extremely long time for them to be useful.
The measurement is the only operation that can change the probability distribution in a circuit. Quantum computation steps are made one at a time when this operation is applied, in practice this operation is not applied in every single computation, and in fact it is used only occasionally.
In a computation step, the gates represented by a circuit or the logic operation that represent the computation can not be represented with another logicalQuantum computation on a quantum computer [[@CR34]]. The quantum computation is a more complex computation but requires much fewer qubits than a classical computation. But the quantum computation that requires the
Q denotes a quantum gate. Here, $m$ is a natural number which denotes the number of qubits in a quantum gate. The subscript denotes the quantum operation that takes two qubits, a qubit pair and apply any quantum logic operation. This equation is an expression for a quantum operation between two quantum gates at any given time. The operator (m+1) mod(`N + m) denotes the addition (mod) operation of one over M = N+m. This operator can be used to apply logical operations to two qubits.N + m). The term operator represents a single-qubit operation (e.g., measurement or logical function), the term $X$ represents the state of a qubit, and $e$ represents the input qubit.
NOT (NOTNOT) gate = NOT (NOT)
QC (Quantum Coherence, QC), a.k.a. Quantum Correlations, operation
CNOT (CNOT) = NOTNOT (NOT)
NOT (NOT) gate = CNOT (CNOT)
NOT (NOT) gate = NOT (NOTNOT)
CNOT (CNOT) = (CNOT) (CNOT) (CNOT)
CNOT gate = CNOT (QC)
D-Wave, a.k.a. the DEC QM (digital quantum computer), use two single-qubit operations: $X$ and $Z$ gates to perform gates on multiple qubits. The D-wave system uses a physical qubit, a superconducting atom called a molecule, to perform quantum logic operations. The qubit is stored directly on the chip and is called ‘storage qubit’. The molecule has $11$ states and the logical logical operators are called $X$ and $Z$. The classical logic operations are performed with three qubits which have four different states ${0, 1, \pm 1}$. The operations $X$, $Z$ and $Z^2$ are performed on the molecule. The logical operation on the molecule is a 2-bit single operation (which is a 1-bit operation on the molecule). The operations on the molecule are $X+Z$ and $XZ$. For more information about D-Wave’s molecules, refer to Digital Quantum Electronics, Quantum Computation and Quantum Information.
The qubit in CQ is in superposition of the two computational states as shown in the figure below. The “qubit” is the quantum information as it is represented by a set of states. Q denotes a quantum logic gate, and is the bit (1), and the third multiplication line applies the measurement result to the ancillary qubit.
CNOT, or 2XNOR gates (Fig 9,a) are NOT gates that can be implemented as two independent XOR gates. The QXNOR gate is a QNOR gate that can be implemented using two QNOR gates that also satisfy an additional property: if the first and second qubits have the same state, then the operation preserves the state, i.e. the first is XOR of the second. Note that CNOT and QXNOR gates (Fig 9,b) are NOT gates, but have two different outputs corresponding to [1,0,0,0] and [0,1,0,0], which corresponds to a NOT gate that applies a measurement in a different basis to the two qubits. Fig 9. The Operation of QNOR and QXNOR The QNOR gates have the following properties: when the first and second qubits have the same state (Fig 9,c), this operation preserves the state (Fig 9,d), i.e., the same results of the measurement are produced for both qubits, and when the two qubits have different states (Fig 9,e), there is no output (Fig 9,f). Note that the same result can be produced when the basis set of the measurement is different because of the xOR operation (Fig 9,c). Fig 9. The Operation of QNOR and QXNOR CNOT, as shown in Fig 11, a CNOT is represented by a gate of three multiplication lines and the measurement represented by a vector representing the sign. The output of the gate is [1,0,0,0] and the measurement result is 1. QNOR, as shown in Fig 11, is represented by a gate of three multiplication lines and the measurement represented by a vector representing both the identity (1) and the sign (Fig 11,g). The output of the gate is [1,0,1,1], representing a qubit to be XOR of the two qubits. QXNOR, as shown in Fig 11, is represented by a gate of three multiplication lines and the measurement represented by a vector representing both the identity (1) and the sign (Fig 11,h). Note that the orthgonal basis and the basis of the CNOT gate are not the same because of the xOR gate (Fig 9). The measure = xNOR
 Figure 4 Using 2 xOR gates to implement the NOT gate:
 Figure 4 Using two 3- qubit NOT gates:
where the first term
 = xOR[δψ~s〉,